4 Answers
4

So you want to calculate $\mathbb{P}[B_1 > B_0 + \varepsilon \;|\; A_1 > A_0 + \varepsilon]$? If you truly have the joint distribution of $A_1$ and $B_1$ and the current prices $A_0$ and $B_0$, this just becomes a simple exercise in integration, by the definition of probability density. Are you asking how to find a conditional probability in general, or is your question about something else?

The main deficiency of this would be if you want a time-varying estimator of conditional probability, since once you've got large $N$, $\hat{p}_N$ would respond very slowly to a sudden clustering of joint positive returns. Here you would want time-varying copulas (not estimated through MLE).
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JaseAug 10 '13 at 13:52